I have the exact same issue, and I am definitely not using a beta version of Chrome. My version number is the same as bbinnard's, except there's no "beta" in it.
I did a little experimentation and discovered that the issue only occurs if "Internet History" (under Applications > Google Chrome) is checked. Running CCleaner with that box checked logs me out of Chrome; when I restart the browser, Chrome complains that it can't find my settings. Logging back in puts everything back to normal.
This is really just an inconvenience, as it's just a matter of logging in manually, but it's weird that it just started happening this week.
Edit: I just discovered that this is being addressed in another thread. Sorry about that!